Problem: Solve for $x$ and $y$ using substitution. ${-6x+2y = -10}$ ${y = -x+11}$
Solution: Since $y$ has already been solved for, substitute $-x+11$ for $y$ in the first equation. ${-6x + 2}{(-x+11)}{= -10}$ Simplify and solve for $x$ $-6x-2x + 22 = -10$ $-8x+22 = -10$ $-8x+22{-22} = -10{-22}$ $-8x = -32$ $\dfrac{-8x}{{-8}} = \dfrac{-32}{{-8}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {y = -x+11}\thinspace$ to find $y$ ${y = -}{(4)}{ + 11}$ $y = -4 + 11$ $y = 7$ You can also plug ${x = 4}$ into $\thinspace {-6x+2y = -10}\thinspace$ and get the same answer for $y$ : ${-6}{(4)}{ + 2y = -10}$ ${y = 7}$